By exploiting nonlocal structure-preserving filters and based on cartoon image decomposition, the proposed method. â Plays an important role in keeping edges ...
DETAIL-PRESERVING COMPRESSIVE SENSING RECOVERY BASED ON CARTOON TEXTURE DECOMPOSITION Thuong Nguyen Canh, Khanh Quoc Dinh, and Byeungwoo Jeon School of Electrical and Computer Engineering, Sungkyunkwan University, KOREA Email: {ngcthuong, dqkhanh, bjeon}@skku.edu
ICIP 2014
1. Abstract
4. TV with nonlocal regularization
Total Variation (TV) preserves edges well but suffers from staircase artifacts and loss of details. Nonlocal structure helps TV to overcome the drawbacks by adding regularization terms. Utilize relationship between cartoon texture image decomposition and residual recovery. We propose a detail-preserving reconstruction method for TV based Compressive Sensing (CS) recovery at low subrate using cartoon texture image decomposition.
=
𝑦
𝐴𝑓 − 𝑦
TV+BM3D[16]: iteratively recover residual, (only texture part)
We use split Bregman [4] method by replacing 𝑉 = 𝐹, 𝐷𝑚 = 𝛻𝑚 𝐹, and adding parameters 𝐵𝑥 , 𝐵𝑦 , 𝑊 𝜇 2 𝛾 2 min 𝑇𝑉 𝐹 + 2 𝑅𝐹𝐺 − 𝑌 2 +2 𝐹 − ℊ(𝐹 2 𝐹,𝑉,𝐷𝑥 ,𝐷𝑦 𝜆 +2
𝐷𝑥 − 𝛻𝑥 𝑉 −
2 𝐵𝑥 2
+
𝜆 2
𝐷𝑦 − 𝛻𝑦 𝑉 − 𝐵𝑦
𝜈 +2
𝐹−𝑉−𝑊
2 2,
2 2
Barbara PSNR
PSNR
ℝ
Measurement
= 𝑅𝐹𝐺 − 𝑌
Subrate Subrate
Subrate
Large size sensing matrix demands High computational complexity Large memory requirement Kronecker CS Separate H & V sensing matrices each of which has smaller size Enable frame based sensing 𝑇 𝑚×𝑛 A=R⊗G 𝑅, 𝐺 ∈ ℝ 2 2
ℊ(. : nonlocal preserving filter
2 2
Peppers
Cameraman PSNR
Signal
2 ×1 𝑛 ℝ
DTV-NLR1: CSRec1: TVNLR1[6],CSRec2: TV[5],Filter: BM3D
Lena 𝑚2 ×1
Sensing matrix
𝑖,𝑗
PSNR(dB) Performance with various recovery methods
= 2 ×𝑛2 𝑚 ℝ
Decomposition based TV recovery (DTV): Exploit nonlocal structure in spatial domain Iteratively recover cartoon and texture TV with spatial nonlocal regularization [6] 𝜇 𝛾 2 2 𝑚𝑖𝑛𝐹 𝑇𝑉 𝐹 + 2 𝑅𝐹𝐺 − 𝑌 2 + 2 𝐹 − ℊ(𝐹 2 , Iterative filtering: Reduce noise & staircase artifact 𝛻𝑥 𝐹 1 + 𝛻𝑦 𝐹 Turn TV output into cartoon image 1 𝑇𝑉 𝐹 = 2 2 1,2: TV[5], Filter: NLM (BM3D) DTV-NL(BM3D): CSRec 𝛻𝑥 𝐹 𝑖,𝑗 + 𝛻𝑦 𝐹 𝑖,𝑗
PSNR
𝑓
5. Proposed Recovery Method
6. Experimental Results
2. Compressive Sensing 𝐴
Digital Media Lab
Subrate
Subrate Proposed (*)
Visual quality with various recovery methods(subrate 0.2)
3.Cartoon Texture Decomposition Split image into cartoon & texture 𝐹 = 𝐹𝐶 + 𝐹𝑇 , th TV’s output at k iteration looks like cartoon image 𝑘 𝑘 𝐹𝐶 = 𝐶𝑆𝑟𝑒𝑐 𝑌 , Decomposition in measurement domain: 𝑘 𝑘 𝑘 𝑌 = 𝑌𝐶 + 𝑌𝑇 , Texture remains in residual meas. 𝑘 𝑘 𝑘 𝐹𝑇 = 𝐶𝑆𝑟𝑒𝑐 𝑌 − 𝑅𝐹𝐶 𝐺 SR=0.2
Ground truth
TVNLR1 [6]
TV+BM3D [16]
DTV-NL*
DTV-BM3D*
DTV-NLR1*
7. Conclusions By exploiting nonlocal structure-preserving filters and based on cartoon image decomposition, the proposed method Plays an important role in keeping edges and textures of image. Outperforms state of the art recovery methods in terms of PSNR and visual quality. Can work with other TV-based recovery methods and structure-preserving filters.
References Lena
Cartoon
Texture
Cartoon and texture images of the proposed method at 8th iteration
[4]. T. Goldstein and S. Osher, “The split Bregman method for L1 regularized problems,” SIAM J. on Imaging Sci., 2009 [5]. S. Shishkin et. al, “Total variation minimization with separable sensing operator,” ICISP, pp. 86–93, 2010. [6]. T. N. Canh et.al, “TV reconstruction for Kronecker CS with a new regularization,” PCS, 2013. [16].Y. Kim et.al, “Video CS using iterative self-similarity modeling and residual reconstruction,” J. of Elect. Imaging, 2013.
Acknowledgment: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No.2011-001-7578)
